Different types of centrifuges intended for processing blood and blood components and also several types of ring bags intended for using in these centrifuges are to be found described in, for example, WO 87/06857, U.S. Pat. No. 5,114,396, U.S. Pat. No. 5,723,050, WO 97/30715, WO 98/35757. Of the centrifuges described therein it is primarily those that are included in the two latter-named patent documents that purpose-intended ring bags are utilized combined with standard secondary bags. In the blood processing bags that are stated in WO 87/06857 and in U.S. Pat. No. 5,114,396 instead of purpose-intended ring bags a more complicated type of bag is included, which consists of a ring formed blood processing chamber manufactured as one unit with a centrally arranged secondary bag. In U.S. Fat. No. 5,723,050 a further description is given of a ring bag intended for the same purpose which, in turn, is secured in a central assembly cover which, on the one hand, gives a central control of the ring bag and, on the other hand, to give room internally for the required secondary bags. In WO 97/30715 and WO 98/35757 it is indicated that the ring bags which are used during centrifuging are secured in the centrifuge by a number of holes on their periphery intended to be fitted over the pins secured in the centrifuge and which are intended for that purpose. This is all well and good but is not sufficiently good as has been shown during the course of the years. The stresses on the bags inner periphery edges, especially when it is only thin pins holding them in place, can be so excessive that the edges of the bags rupture.